PRP Records

Probable Primes Top 10000

(181746 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
900112^47861-3551651Lelio R Paula12/2012
90026^66369-2681351646Enzo Doria03/2013
9003Phi(83967,10)/227248288951639Maksym Voznyy01/2010
90042^171524+15351634Lelio R Paula02/2011
9005(2^171516-509203)/486951628Lelio R Paula05/2012
9006(12589^12589+323)/2^5/351613Makoto Morimoto07/2016
90075*10^51608-8151609Robert Price04/2017
9008(lucasV(1,2,342870)+2)/(13*25933*242617)51597Mike Oakes03/2017
900910171^12872-12872^1017151583Norbert Schneider04/2017
90102^171351-11267751582Enzo Doria06/2014
9011(12583^12583+1695)/2/11^2/753508951579Makoto Morimoto07/2016
90129818^12919-12919^981851573Norbert Schneider05/2017
9013(3^108091+7)/38251570Lelio R Paula03/2012
90152^171287-318751563Yves Minet04/2009
9014-lucasV(-1,2,342569)51563Mike Oakes02/2017
90162^171280-103070951561Paul Bourdelais11/2012
901713300^7527+7527^1330051560Hans Havermann05/2016
90182^171268+7371151557Enzo Doria04/2016
9019(17*2^171266+1)/696351554Lelio R Paula01/2012
9020(1964814^8192+1)/6553751551Lelio R Paula06/2013
90214*10^51530-6351531Robert Price12/2016
90223*6^66216-551527Lelio R Paula09/2014
902312569^12569+54051525Makoto Morimoto07/2016
90242^171152-245951522Yves Minet07/2014
9025(13*10^51511-1)/351512Robert Price12/2014
90265*10^51508+351509Dmitry Domanov11/2010
90273^107919-4651491Lelio R Paula07/2012
90284*10^51489+8751490Robert Price05/2016
9029(22699*2^171030+1)/302951487Lelio R Paula05/2014
90302^171028-323951485Yves Minet12/2014
90312^170992-95420951474Paul Bourdelais11/2012
903276^27367+7551473Norbert Schneider11/2012
90336007^13620-10251466Enzo Doria07/2012
9034gcd(V(923445),5*F(184689)*(F(184689)-1)+1)51462Serge Batalov04/2015
9035t(194442)51459Robert Price08/2014
9036(22*10^51457+161)/351458Robert Price02/2017
90379^53921+8^(53921+1)51454Robert Price06/2016
90392^170921-1699551453Lelio R Paula08/2011
90382^170922-213551453Yves Minet06/2013
90404357^14138-12051451Enzo Doria06/2012
9041153^23550+251450Lelio R Paula05/2013
9042(3^107833+2)/2551449Lelio R Paula03/2012
90437*10^51440-4751441Robert Price02/2017
9044(10^51431-3^51431)/751431Robert Price06/2011
9045U(250849)51425Michael Porter08/2007
9046(86*10^51424-41)/951425Robert Price11/2015
904812^47649+751422Lelio R Paula12/2012
9047(25*10^51421+11)/951422Robert Price03/2015
90493^107768+266051419Lelio R Paula07/2012
90502^170784-655551412Lelio R Paula05/2009
9051(-lucasV(1,2,341584)-2)/7951412Mike Oakes03/2017
905251^30106+251409Lelio R Paula05/2013
90535^73546-1280651407Enzo Doria02/2013
9054(12545^12545+12546^12546)/(1584571*19137767639)51404Walter Nissen09/2014
9055(3^107735-4)/43151401Lelio R Paula03/2012
905620^39505-648351398Enzo Doria03/2013
90572^170736-1519751397Enzo Doria04/2013
90582^170737-382351397Yves Minet04/2017
9059(12541^12541+393)/2/56351395Makoto Morimoto07/2016
90609^53857-8^5385751393Jean-Louis Charton11/2004
90615^73524-1442651392Enzo Doria02/2013
90622^170712+24351390Lelio R Paula10/2011
9063(15*2^170713+1)/179351388Lelio R Paula07/2012
9064(2^170702+9)/126151384Lelio R Paula01/2012
9065283^20956+20956^28351380Norbert Schneider08/2014
90662^170665-3151376Lelio R Paula01/2011
906711^49330-1251372Lelio R Paula01/2013
9068(25*10^51366-73)/351367Robert Price09/2016
90695^73486-2^7348751365Mike Oakes10/2010
9070(10^51364+119)/351364Serge Batalov12/2014
907115^43672+6851363Lelio R Paula01/2013
90722^170609-11314351359Enzo Doria07/2014
9073760^17827-759^1782751357Jean-Louis Charton12/2010
9074(22699*2^170592+1)/443551355Lelio R Paula05/2014
90758*7^60767+351355Lelio R Paula09/2014
90765^73452-2064651341Enzo Doria03/2013
90772^170531-23040751335Gary Barnes08/2009
907835^33243-211251330Enzo Doria03/2013
9079(1845768^8192+1)/6553751328Lelio R Paula06/2013
908013^46072+4251322Lelio R Paula01/2013
908114^44778-9551322Lelio R Paula01/2013
908211008^12697+12697^1100851318Norbert Schneider01/2016
9083t(180039)51312Robert Price09/2014
90842^170444-44351309Yves Minet05/2013
9085(-lucasV(1,2,340915)+2)/(340913*4220189*8187163)51294Mike Oakes03/2017
9086(2*10^51285-71)/351285Robert Price01/2017
9087(1819288^8192+1)/6553751277Lelio R Paula06/2013
90888907^12982-12982^890751276Norbert Schneider06/2017
90895^73350+2851270Lelio R Paula10/2012
90903^107450+251267Mike Oakes11/2009
90912^170296+253351265Henri Lifchitz07/2004
90922^170293+7648151264Enzo Doria05/2016
909311835^12584+12584^1183551257Norbert Schneider11/2015
9094(12511^12511+193)/2^5/3937151256Makoto Morimoto07/2016
909612^47489+47489^1251250Serge Batalov02/2012
909514637^3172+3172^1463751250Hans Havermann04/2016
9097(2^170245+7)/951248Lelio R Paula02/2012
90985^73308-1992651241Enzo Doria03/2013
90998966^12963-12963^896651238Norbert Schneider06/2017
91003*2^170203+551237Lelio R Paula02/2014
91015^73300+4651235Lelio R Paula10/2012
91022^170167+7151226Lelio R Paula01/2011
91032^170140-1507751218Enzo Doria04/2013
910415^43542-4651210Lelio R Paula01/2013
91062^170111-101751209Lelio R Paula06/2008
91054*10^51208-8751209Robert Price03/2017
910714^44679+8351208Lelio R Paula01/2013
910810^51207+10014751208Patrick De Geest06/2016
910910^51207-80151207Robert Price04/2016
9110t(170300)51191Robert Price03/2015
911111966^12553-12553^1196651191Norbert Schneider11/2016
911214670^3083+3083^1467051184Hans Havermann04/2016
911399^25644-9851177Norbert Schneider07/2013
911413211^7468+7468^1321151169Hans Havermann04/2016
9115(2^169969-1017)/3551165Lelio R Paula01/2012
91165*10^51163-751164Dmitry Domanov11/2010
9117(73*10^51162-1)/951163Robert Price01/2015
91182^169899+6351145Lelio R Paula05/2009
91192^169898+51351145Lelio R Paula05/2009
91203^107186-1238851141Enzo Doria02/2013
9121(12487^12487+173)/2^2/3/2917/3463/4448351140Makoto Morimoto07/2016
91223*6^65715-751137Lelio R Paula09/2014
9123116^24768+11551133Norbert Schneider10/2013
912435^33113-402651129Enzo Doria03/2013
9125(13*2^169830-1)/8447751121Lelio R Paula01/2014
9126(46*10^51111-1)/951112Serge Batalov10/2014
912715^43452-3451104Lelio R Paula01/2013
91282^169750-13751100Lelio R Paula01/2011
91292^169739+9406551097Lelio R Paula10/2011
913115^43442-2651092Lelio R Paula01/2013
91325^73096-1700651092Enzo Doria02/2013
913010^51091+7160151092Patrick De Geest07/2017
913310^51091-70151091Robert Price06/2017
9134(-lucasV(1,2,339439)-2)/(79*83)51088Mike Oakes03/2017
91352^169706-27055151087Gary Barnes08/2009
9136(2^169696+5)/2151083Lelio R Paula01/2012
9137(1722520^8192+1)/6553751082Syoichiro Yamada01/2009
913811^49051-876051082Enzo Doria02/2013
9139(24737*2^169672+1)/2751080Lelio R Paula05/2014
91402^169677+1609551078Lelio R Paula05/2009
91412^169659-13551073Lelio R Paula01/2011
91422^169638-11318351067Enzo Doria07/2014
9143(29*2^169622-1)/234653118551054Lelio R Paula01/2014
9144(10^51054+17)/951054Robert Price10/2014
91458329^13022-13022^832951054Norbert Schneider07/2017
9146(24737*2^169577+1)/551052Lelio R Paula05/2014
914711^49021-7851051Lelio R Paula01/2013
914818^40669+6151051Lelio R Paula01/2013
914914038^4327+4327^1403851045Hans Havermann02/2016
91502^169555-15951042Lelio R Paula01/2011
915191^26054-251041Lelio R Paula08/2013
9152Phi(101775,10)/162840151034Makoto Kamada05/2015
915397*10^51027-351029Robert Price01/2017
91542^169499-264751025Yves Minet07/2014
91555*6^65567+751022Lelio R Paula09/2014
915614763^2858+2858^1476351022Hans Havermann08/2015
915724^36966-147751021Enzo Doria03/2013
9158(78557*2^169464+1)/16052751014Lelio R Paula06/2014
9159(34*10^51008-43)/951009Ray Chandler09/2010
916010^51004+12842751005Patrick De Geest08/2009
916210^51004-11351004Milton L. Brown12/2008
916110^51003+1695151004Patrick De Geest08/2009
916310^51003-7960151003Milton L. Brown12/2008
916410^51003-8083151003Milton L. Brown12/2008
916510^51002+887751003Patrick De Geest08/2009
916710^51002-1054151002Milton L. Brown11/2008
916610^51001+5205151002Patrick De Geest08/2009
916810^51001-15868751001Milton L. Brown10/2008
91692*10^51000+9351001Robert Price07/2016
9172(2^169416+5)/350999Lelio R Paula01/2012
9170(49*10^50998+41)/950999Robert Price07/2015
917113292^6867+6867^1329250999Hans Havermann02/2016
9173(35*10^50997-71)/950998Robert Price05/2015
91746^65536+2*97878-150997Jiahao He05/2017
917529^34871-28^3487150996Robert Price09/2012
917676^27112-7550993Norbert Schneider11/2012
9177(70^27631-1)/6950981Richard Fischer08/2017
9178(12451^12451+1345)/2^2/19/89/139/697750980Makoto Morimoto07/2016
917910736^12645-12645^1073650971Norbert Schneider12/2016
9181(1017*2^169315-1)/971550968Lelio R Paula03/2015
91807^60309-6^(60309+1)50968Robert Price06/2016
91832^169267+9950955Lelio R Paula07/2009
91825*2^169264+350955Lelio R Paula02/2014
9184t(192517)50950Robert Price08/2014
918510^50943+62445150944Robert Price03/2015
918610^50943+5440950944Patrick De Geest02/2016
918710^50943-10055950943Patrick De Geest03/2016
91882^169206-364550937Lelio R Paula05/2009
91892^169196-11257750934Enzo Doria06/2014
919020^39146-348350931Enzo Doria03/2013
919110^50929+1684950930Patrick De Geest01/2012
919310^50929-5150929Robert Price05/2011
91927^60264+4850929Lelio R Paula10/2012
91952^169167+129950925Lelio R Paula05/2009
919410103^12717-10050925Enzo Doria07/2012
91963^106721-13050919Lelio R Paula07/2012
919818225^622+622^1822550917Anatoly F. Selevich11/2006
9197(10223*2^169138+1)/111350917Lelio R Paula05/2014
91997*2^169125+950913Lelio R Paula02/2014
9200(47*2^169123+1)/2950912Lelio R Paula03/2015
920120^39131+9350911Lelio R Paula01/2013
9202(21*27^35567-94921)/2650910Curtis Bright05/2015
9203(7*2^169124-1)/954950909Lelio R Paula01/2014
9204(12433^12433+809)/2/3/1150907Makoto Morimoto07/2016
920513693^5212+5212^1369350897Hans Havermann02/2016
92067*5^72813+650895Lelio R Paula09/2014
92075*10^50890-8150891Robert Price04/2017
92083^106656-1202850888Enzo Doria02/2013
9209(2^169028+3)/25950881Lelio R Paula01/2012
92102^169000-112750875Yves Minet05/2013
921119^39780+1650869Lelio R Paula01/2013
9212(19*2^168960+1)/550863Lelio R Paula07/2012
9213(-lucasV(1,2,337937)-2)/(3^2*11)50863Mike Oakes02/2017
921511^48840+4650862Lelio R Paula01/2013
9214(5*10^50861-107)/350862Robert Price01/2017
921620^39087-420350854Enzo Doria03/2013
9217(12421^12421+1339)/2^4/5/43/15750848Makoto Morimoto07/2016
92182^168907-54444750847Paul Bourdelais11/2012
921919312^429+429^1931250839Anatoly F. Selevich12/2006
92205^72716-1322650827Enzo Doria02/2013
92212^168823+102550821Lelio R Paula01/2009
92227*10^50818-8950819Robert Price01/2017
92232^168811+15015*16881150818Henri Lifchitz02/2005
92242^168813-283350818Yves Minet09/2014
9225(12413^12413+3221)/2/8950816Makoto Morimoto07/2016
92262^168795+538550813Lelio R Paula05/2009
92274*3^106483+550806Lelio R Paula03/2014
922813^45606+450803Lelio R Paula01/2013
922913^45606-3850803Lelio R Paula01/2013
92302^168746+5890550798Lelio R Paula05/2009
9231(16*10^50795-43)/950796Robert Price02/2015
9232gcd(V(615445),5*F(123089)*(F(123089)-1)+1)50794Serge Batalov04/2015
92337*10^50789-4750790Robert Price02/2017
92342^168717-72952350789Paul Bourdelais11/2012
9235(12409^12409+136)/5^2/13/5647/47327950788Makoto Morimoto07/2016
9236(21*2^168652-1)/21550769Lelio R Paula01/2014
92372^168629+1290950763Lelio R Paula01/2011
92389328^12787+12787^932850762Norbert Schneider01/2016
92392^168627+7311350762Enzo Doria04/2016
92402^168623+4733350761Yves Minet02/2010
9241(12401^12401+154)/3^2/5/31/59/67/97/761/863/1214350745Makoto Morimoto07/2016
9242(lucasV(1,2,337126)+2)/(5*11)50739Mike Oakes02/2017
92438544^12901-12901^854450723Norbert Schneider05/2017
9244(17^41221+1)/1850720Paul Bourdelais03/2010
924510^50711+750712Jason Earls12/2007
924610^50711-31796950711Patrick De Geest04/2009
9247(17^41213+3^41213)/2050710Robert Price08/2013
9248(12391^12391+58)/59/211/782350710Makoto Morimoto07/2016
924947779!4+102450708Robert Price08/2017
92502^168431-15950703Lelio R Paula01/2011


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 14 2017 17:05 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!